论文标题
热带后代不变的有线约束
Tropical descendant invariants with line constraints
论文作者
论文摘要
通过对应定理，可以根据热带几何形状来计算平面的理性log gromov。在许多情况下，存在多种算法要热门计算：例如，有（广义）晶格路径计数和落地图技术。到目前为止，存在算法的案例并未扩展到非平稳的有理后代对数Gromov- witten不变性的，即\ \ \ \ \ psi条件不必与对点的评估相匹配的情况。理性的后代对数格罗莫夫（Gromov）的案例 - 持久的不变式满足点条件（没有PSI条件）和一个对任何功率和线路结合的PSI条件都起着特别重要的作用，因为它在镜像对称性中显示为$ j $ - 功能的系数。我们提供递归公式来通过热带方法计算这些数字。我们的方法灵感来自WDVV方程的热带证明。我们还将研究扩展到涉及两条线的计数，都与PSI条件配对，并以功率为ONE。
Via correspondence theorems, rational log Gromov--Witten invariants of the plane can be computed in terms of tropical geometry. For many cases, there exists a range of algorithms to compute tropically: for instance, there are (generalized) lattice path counts and floor diagram techniques. So far, the cases for which there exist algorithms do not extend to non-stationary rational descendant log Gromov--Witten invariants, i.e.\ those where Psi-conditions do not have to be matched up with the evaluation of a point. The case of rational descendant log Gromov--Witten invariants satisfying point conditions (without Psi-conditions) and one Psi-condition of any power combined with a line plays a particularly important role, since it shows up in mirror symmetry as coefficients of the $J$-function. We provide recursive formulas to compute those numbers via tropical methods. Our method is inspired by the tropical proof of the WDVV equations. We also extend our study to counts involving two lines, both paired up with a Psi-condition, appearing with power one.
